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Sudoku Solution Path

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R3C3 is the only square in row 3 that can be <4>
R4C4 is the only square in row 4 that can be <9>
R6C3 is the only square in row 6 that can be <1>
R6C6 is the only square in row 6 that can be <3>
R7C6 is the only square in row 7 that can be <1>
R8C8 is the only square in row 8 that can be <4>
R9C2 is the only square in column 2 that can be <5>
R6C4 is the only square in column 4 that can be <8>
R6C7 can only be <2>
R1C7 is the only square in column 7 that can be <3>
R1C8 is the only square in row 1 that can be <8>
R5C8 can only be <5>
R7C3 is the only square in column 3 that can be <3>
Squares R1C3 and R1C5 in row 1 and R9C3 and R9C5 in row 9 form a Simple X-Wing pattern on possibility <6>. All other instances of this possibility in columns 3 and 5 can be removed.
   R8C5 - removing <6> from <269> leaving <29>
Squares R8C2 and R8C5 in row 8 form a simple locked pair. These 2 squares both contain the 2 possibilities <29>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
   R8C1 - removing <29> from <2689> leaving <68>
   R8C9 - removing <2> from <268> leaving <68>
Squares R2C5 and R2C9 in row 2 and R5C5 and R5C9 in row 5 form a Simple X-Wing pattern on possibility <7>. All other instances of this possibility in columns 5 and 9 can be removed.
   R3C9 - removing <7> from <257> leaving <25>
Squares R3C1 and R3C7 in row 3 and R7C1 and R7C7 in row 7 form a Simple X-Wing pattern on possibility <9>. All other instances of this possibility in columns 1 and 7 can be removed.
   R2C1 - removing <9> from <239> leaving <23>
   R9C7 - removing <9> from <89> leaving <8>
R4C7 can only be <7>
R8C9 can only be <6>
R4C6 can only be <2>
R5C9 can only be <8>
R8C1 can only be <8>
R4C3 can only be <8>
R3C6 can only be <7>
R5C5 can only be <7>
R2C9 is the only square in row 2 that can be <7>
Squares R2C1 and R5C1 in column 1 form a simple locked pair. These 2 squares both contain the 2 possibilities <23>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
   R3C1 - removing <2> from <269> leaving <69>
   R7C1 - removing <2> from <269> leaving <69>
Squares R5C1, R5C2, R2C1 and R2C2 form a Type-1 Unique Rectangle on <23>.
   R2C2 - removing <23> from <1239> leaving <19>
R2C1 is the only square in row 2 that can be <3>
R5C1 can only be <2>
R5C2 can only be <3>
Intersection of block 1 with row 1. The value <2> only appears in one or more of squares R1C1, R1C2 and R1C3 of block 1. These squares are the ones that intersect with row 1. Thus, the other (non-intersecting) squares of row 1 cannot contain this value.
   R1C5 - removing <2> from <126> leaving <16>
The puzzle can be reduced to a Bivalue Universal Grave (BUG) pattern, by making this reduction:
   R9C5=<69>
These are called the BUG possibilities. In a BUG pattern, in each row, column and block, each unsolved possibility appears exactly twice. Such a pattern either has 0 or 2 solutions, so it cannot be part of a valid Sudoku
When a puzzle contains a BUG, and only one square in the puzzle has more than 2 possibilities, the only way to kill the BUG is to remove both of the BUG possibilities from the square, thus solving it
   R9C5 - removing <69> from <269> leaving <2>
R9C3 can only be <6>
R9C8 can only be <9>
R2C5 can only be <1>
R8C5 can only be <9>
R7C4 can only be <6>
R2C8 can only be <2>
R7C7 can only be <5>
R2C2 can only be <9>
R1C5 can only be <6>
R3C9 can only be <5>
R3C7 can only be <9>
R7C9 can only be <2>
R7C1 can only be <9>
R3C4 can only be <2>
R8C2 can only be <2>
R1C3 can only be <2>
R1C2 can only be <1>
R3C1 can only be <6>


 

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